Friday, February 26, 2010

40,000 Talents

I normally wouldn't blog my response to this post, but the circumstances are such that the comment might not survive moderation, and I would like there to be a record (I draw a lesson from all this at the end).

For the last several days, I’ve been wondering about Arrian’s assertion in his life of Alexander the Great, that at the capture of Persepolis, Alexander and his army captured 40,000 talents of silver.

Now, a talent is a measure from ancient times, about 58 pounds of silver or gold. So I’ve been wondering, how much is that?

I’ve asked a few colleagues, and it turns out that people are curious. Not as curious as I am perhaps, but curious. But it’s been gnawing at my insides for a few days, and I didn’t know how to solve the problem.

Then I realized, I DID know. I used Wolfram|Alpha. It turns out that 40,000 talents of silver is about 2,320,000 pounds. And that weight of silver is 96.4 cubic meters – not quite a cubic kilometer of silver, but close.

You shouldn’t need to look up 40,000 times 58. Because 4 x 6 is 24, 4 x 2 = 8, you know the amount is 2,400,000 – 80,000 = 2,320,000. No calculator needed.

You might not know that your silver is a bit more than 10 grams per cubic centimeter (CC) http://en.wikipedia.org/wiki/Silver , so you may have to look up the fact that just under a million kilograms of silver (1 kg = 2.5 pounds, roughly) is just under 100 cubic meters.

But there is no excuse for saying that 96.4 cubic meters is close to a cubic kilometer. First of all, a kilometer is 1,000 meters, not 100. Second, a cubic kilometer = 1000 meters x 1000 meters x 1000 meters = 1,000,000,000 cubic meters. One billion cubic meters, not 100 cubic meters.

The value of silver is generally around 15 dollars per ounce (today it’s about $16.50 – http://silverprice.org/silver-price-history.html ) and there are 12 avoirdupois troy ounces to a pound, so a pound of silver is worth $180. Say, about $200 today.

200 x 2 million = 400 million, so there’s no way $200 x 2,320,000 is $2.6 billion. More like $464 million. Silver would have to be priced at $60 per ounce to be worth that much. Silver peaked at about $50 an ounce once in 1980, but has otherwise never been close.

To put things in perspective, if I had a 1 gram dime to sell, your calculations would result in it being 1 million grams, which you would buy from me for $12,000.

(Just as an aside - this was not part of my response - I have often argued that 'knowing' is an act of recognizing and not remembering. This is a case in point. A person that merely remembers must execute a series of calculations, in which there is a lot of room for error. But a person who knows can recognize errors that are that large.

Such a person looks at 40K x 60 and just sees 2.4 million. Such a person looks at 96 cubic meters and just sees that it is not remotely a cubic kilometer (it is actually roughly 10 meters long by 3 meters wide by 3 meters high - roughly the size of a semi-trailer). When you learn math - or anything! - by rote, you do not learn to 'just see' - you do not develop 'knowledge as recognition'.)

3 comments:

The comment did survive moderation, because I think it's important to remember our egregious errors as well as our successes. I DID edit the entry, as you'll see going back to it, to reflect your changes.

I do math largely as a process of remembering, rather than recognizing, as you describe it. It would be easy to blame my mathematical innumeracy on others, but the truth is I didn't study it enough in the past — and I concentrated on geometry when I did study mathematics, mostly flat-plane geometry.

As a result, I don't just see 2.4 million. I don't see 96 cubic meters as a semi-trailer (though I wish I did, and I may now).

My failures at math have been a consistent disappointment both to me and to my father, and I regularly embarrass myself in this way when I do math in a public or private arena.